Re: Indices of refraction are complex??

[Doug Craigen <dcc@ESCAPE.CA>]

Digby Willard wrote:
> > Remember, also, that indices of refraction are complex!
>
> That's news to me.  Might be something I once knew, but it rings no bells.
> My understanding of indices of refraction comes from Huygens' Principle and
> Snell's Law, as applied at the high school level.
>
> Could you elaborate a bit?  If possible, keep the elaboration to advanced
> high school level or a bit beyond.

Think of the "imaginary" part of "n" as the absorption coefficient - or
perhaps as the "cause" of it.  If "n" is complex, then so is the wave
speed, hence so is the wave vector "k".  So in the complex notation y =
RealPart[Aexp(i[kx-wt])] (pasted in from John Denker's summary), k has
both real and imaginary parts.  The imaginary part will lead to i*i=-1 -
you will be multiplying by exp(-alpha*x)... the wave decays
exponentially with distance into the material.

Again the point is not that "n" really has an imaginary part, but that
this is all nothing but math to do calculations, and writing an
imaginary part onto "n" is an elegant and natural (when you do the full
EM solution) fashion to include absorption effects.

()-()-()-()-()-()-()-()-()-()-()-()-()-()-()-()

Doug Craigen
          http://www.dctech.com/physics/